EDA for Health Care Sector Fund

The Health Care Sector Fund (XLV) is an exchange-traded fund (ETF) that tracks the performance of companies in the healthcare sector, including pharmaceuticals, healthcare equipment and supplies, healthcare providers and services, biotechnology, and life sciences tools and services. This fund provides investors with a convenient way to invest in a diverse range of healthcare companies, enabling them to gain exposure to this sector without having to buy individual stocks. The XLV has been a popular choice among investors looking for a defensive play, given the healthcare sector’s reputation for being relatively resilient during market downturns.

Time Series Plot

Code

# get data
options("getSymbols.warning4.0"=FALSE)
options("getSymbols.yahoo.warning"=FALSE)


data = getSymbols("XLV",src='yahoo', from = '2010-01-01',to = "2023-03-01")

df <- data.frame(Date=index(XLV),coredata(XLV))

# create Bollinger Bands
bbands <- BBands(XLV[,c("XLV.High","XLV.Low","XLV.Close")])

# join and subset data
df <- subset(cbind(df, data.frame(bbands[,1:3])), Date >= "2010-01-01")

#export the data 
XLV_data <- df
write.csv(XLV_data, "DATA/CLEANED DATA/XLV_raw_data.csv", row.names=FALSE)

# colors column for increasing and decreasing
for (i in 1:length(df[,1])) {
  if (df$XLV.Close[i] >= df$XLV.Open[i]) {
      df$direction[i] = 'Increasing'
  } else {
      df$direction[i] = 'Decreasing'
  }
}

i <- list(line = list(color = '#FF7F50'))
d <- list(line = list(color = '#7F7F7F'))

# plot candlestick chart

fig <- df %>% plot_ly(x = ~Date, type="candlestick",
          open = ~XLV.Open, close = ~XLV.Close,
          high = ~XLV.High, low = ~XLV.Low, name = "XLV",
          increasing = i, decreasing = d) 
fig <- fig %>% add_lines(x = ~Date, y = ~up , name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands",
            hoverinfo = "none", inherit = F) 
fig <- fig %>% add_lines(x = ~Date, y = ~dn, name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands", inherit = F,
            showlegend = FALSE, hoverinfo = "none") 
fig <- fig %>% add_lines(x = ~Date, y = ~mavg, name = "Mv Avg",
            line = list(color = '#E377C2', width = 0.5),
            hoverinfo = "none", inherit = F) 
fig <- fig %>% layout(yaxis = list(title = "Price"))

# plot volume bar chart
fig2 <- df 
fig2 <- fig2 %>% plot_ly(x=~Date, y=~XLV.Volume, type='bar', name = "XLV Volume",
          color = ~direction, colors = c('#FF7F50','#7F7F7F')) 
fig2 <- fig2 %>% layout(yaxis = list(title = "Volume"))

# create rangeselector buttons
rs <- list(visible = TRUE, x = 0.5, y = -0.055,
           xanchor = 'center', yref = 'paper',
           font = list(size = 9),
           buttons = list(
             list(count=1,
                  label='RESET',
                  step='all'),
             list(count=3,
                  label='3 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 MO',
                  step='month',
                  stepmode='backward')
           ))

# subplot with shared x axis
fig <- subplot(fig, fig2, heights = c(0.7,0.2), nrows=2,
             shareX = TRUE, titleY = TRUE)
fig <- fig %>% layout(title = paste("Health Care Sector Fund Stock Price: JAN 2010 - March 2023"),
         xaxis = list(rangeselector = rs),
         legend = list(orientation = 'h', x = 0.5, y = 1,
                       xanchor = 'center', yref = 'paper',
                       font = list(size = 10),
                       bgcolor = 'transparent'))

fig

The Health Care Sector Fund (XLV) has experienced significant fluctuations and trends from 2010 to March 2023. The fund has shown an upward trend with several dips in between due to various reasons such as political uncertainty, global pandemic, and regulatory changes. The fund experienced a sharp drop in 2011 due to the debt ceiling crisis, but quickly recovered by the end of the year. It showed a steady increase until the end of 2015, followed by a sharp dip in 2016 due to the U.S. presidential election.

In 2020, the COVID-19 pandemic caused a significant impact on the healthcare sector, leading to a sharp dip in the XLV fund’s value. However, it quickly bounced back and reached an all-time high in February 2021. The fund continued to experience fluctuations due to regulatory changes and global events such as the Biden administration’s announcement on drug pricing and the vaccine rollout. Overall, the Health Care Sector Fund has been influenced by various factors that have impacted the healthcare industry, resulting in significant fluctuations in its value.

For stock prices, a multiplicative decomposition is typically preferred because the percentage changes in stock prices tend to be more important than the absolute changes. Additionally, stock prices tend to exhibit non-constant variance, meaning that the variance of the series changes over time. A multiplicative decomposition can handle this non-constant variance more effectively than an additive decomposition.

Decomposed Time Series

Decomposition Plot

Code

#time series data
myts<-ts(df$XLV.Adjusted,frequency=252,start=c(2010,01,01), end = c(2023,3,1)) 
#original plot for time series data
orginial_plot <- autoplot(myts,xlab ="Year", ylab = "Adjusted Closing Price", main = "Health Care Sector Fund Stock price: JAN 2010 - March 2023")
#decompose the data
decompose = decompose(myts, "multiplicative")
#decomposition plot
autoplot(decompose)

Adjusted Decomposition Plot

Code

#adjusted plot
trendadj <- myts/decompose$trend
decompose_adjtrend_plot <- autoplot(trendadj,ylab='trend') +ggtitle('Adjusted trend component in the multiplicative time series model')
seasonaladj <- myts/decompose$seasonal
decompose_adjseasonal_plot <- autoplot(seasonaladj,ylab='seasonal') +ggtitle('Adjusted seasonal component in the multiplicative time series model')
grid.arrange(orginial_plot, decompose_adjtrend_plot,decompose_adjseasonal_plot, nrow=3)

The adjusted seasonal component tend to have upward trend till 2019 and drops during the covid period and there is more variability in the model when compared to the original plot where the variation during the years but the adjusted trend then to have more fluctuation showing no trend when compared to the original plot.

Lag Plots

Daily Time Lags

Code

#Lag plots 
gglagplot(myts, do.lines=FALSE, lags=1)+xlab("Lag 1")+ylab("Yi")+ggtitle("Lag Plot for Health Care Sector Fund Stock JAN 2010 - March 2023")

Monthly Time Lags

Code

#montly data
mean_data <- df %>% 
  mutate(month = month(Date), year = year(Date)) %>% 
  group_by(year, month) %>% 
  summarize(mean_value = mean(XLV.Adjusted))
month<-ts(mean_data$mean_value,start = c(2010, 1),frequency = 12)
#Lag plot
ts_lags(month)

The first lag plot shows the daily time lags of the Health Care Sector Fund stock price from JAN 2010 to March 2023. The plot indicates that there is a strong positive correlation between the current value and the previous day’s value, as seen by the points clustering along the diagonal line. This suggests that the stock price has a positive autocorrelation at a lag of one day.

The second lag plot shows the monthly time lags of the mean value of the Health Care Sector Fund stock price from JAN 2010 to March 2023. The plot indicates that there is a positive correlation between the current value and the value from the previous month. This suggests that the mean value of the stock price has a positive autocorrelation at a lag of one month.

Overall, the lag plots indicate that there is a positive autocorrelation present in the Health Care Sector Fund stock price data, with the strongest correlation observed in the daily time series.

Seasonality

Seasonal Heatmap

Code

# Create seasonal plot
ts_heatmap(month, color = "GnBu",title = 'Seasonality Heatmap of Health Care Sector Fund Stock Jan 2010 - March 2023')

Seasonal Line plot

Code

# Create a line graph for each year with months on the x-axis
ggseasonplot(month, datecol = "date", valuecol = "value")+ggtitle("Seasonal Yearly Plot for Health Care Sector Fund Stock Jan 2010 - March 2023")

The Seasonality Heatmap for the Health Care Sector Fund Stock JAN 2010 - March 2023 does not reveal any clear seasonality in the data. The heatmap shows the mean value of the time series for each month and year combination, with the darker colors indicating higher values. The lack of clear patterns or darker colors in specific months or years suggests that there is no consistent seasonal pattern in the data. However, the yearly line graph shows a slight upward trend in the stock price from 2010 to 2023, but does not show any clear seasonality. Each year’s data is represented by a line, and the months are plotted on the x-axis. Overall, the lack of clear seasonality in both the heatmap and yearly line graph suggests that other factors beyond seasonality are driving the stock price fluctuations.

Moving Average

4 Month MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,5), series="4 Month MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Health Care Sector Fund Stock JAN 2010 - March 2023(4 Month Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","4 Month MA"="red"),
                      breaks=c("Data","4 Month MA"))
ma

1 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,13), series="1 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Health Care Sector Fund Stock JAN 2010 - March 2023(1 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","1 Year MA"="red"),
                      breaks=c("Data","1 Year MA"))
ma

3 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,37), series="3 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Health Care Sector Fund Stock JAN 2010 - March 2023(3 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","3 Year MA"="red"),
                      breaks=c("Data","3 Year MA"))
ma

5 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,61), series="5 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Health Care Sector Fund Stock JAN 2010 - March 2023(5 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","5 Year MA"="red"),
                      breaks=c("Data","5 Year MA"))
ma

The four plots show the Health Care Sector Fund stock prices from JAN 2010 to March 2023, along with the moving averages for 4 months, 1 year 3 years and 4 years. As the window of the moving average increases, the smoother the trend line becomes, reducing the impact of noise and fluctuations in the original time series.

The 4-month moving average plot shows frequent fluctuations in the stock price, with the trend line following the general direction of the time series. The 1-year moving average plot shows a smoother trend, following the overall upward trend of the stock price.

The 1-year moving average plot shows a similar trend to the 4-month plot but is even smoother, with fewer fluctuations. Finally, the 5-year moving average plot shows the smoothest trend, with an almost constant upward slope.As the moving average window increases, the smoother trend allows for a clearer identification of the general trend of the Health Care Sector Fund stock prices over time. From the moving average obtained above we can see that there is upward tend in the stock price of Health Care Sector Fund.

Autocorrelation Time Series

ACF

Code

#ACF for  data
ggAcf(month)+ggtitle("ACF Plot for Health Care Sector Fund Stock JAN 2010 - March 2023")

PACF

Code

#PACF for data
ggPacf(month)+ggtitle("PACF Plot for Health Care Sector Fund Stock JAN 2010 - March 2023")

ADF Test

Code

#check the stationarity
tseries::adf.test(month)

    Augmented Dickey-Fuller Test

data:  month
Dickey-Fuller = -1.8408, Lag order = 5, p-value = 0.6427
alternative hypothesis: stationary

In the plot of autocorrelation function, which is the acf graph for monthly data, there are clear autocorrelation in lag. The above lag plots and autocorrelation plot indicates seasonality in the series, which means the series is not stationary. It was also verified using Augmented Dickey-Fuller Test which tells us that as the p value is greater than 0.05, the series is not stationary.

Detrend and Differenced Time Series

Linear Fitting Model

Code

fit = lm(myts~time(myts), na.action=NULL) 
summary(fit) 

Call:
lm(formula = myts ~ time(myts), na.action = NULL)

Residuals:
     Min       1Q   Median       3Q      Max 
-28.9902  -4.9914  -0.9621   4.6109  22.5840 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.708e+04  6.474e+01  -263.8   <2e-16 ***
time(myts)   8.504e+00  3.210e-02   264.9   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6.905 on 3277 degrees of freedom
Multiple R-squared:  0.9554,    Adjusted R-squared:  0.9554 
F-statistic: 7.016e+04 on 1 and 3277 DF,  p-value: < 2.2e-16

ACF Plot

Code

# plot ACFs
plot1 <- ggAcf(myts, 48, main="Original Data: Health Care Sector Fund Stock Stock Price")
plot2 <- ggAcf(resid(fit), 48, main="Detrended data")
plot3 <- ggAcf(diff(myts), 48, main="First differenced data")
grid.arrange(plot1, plot2, plot3, nrow=3)

The estimated slope coefficient β1, 1.6399 With a standard error of 0.1219, yielding a significant estimated increase of stock price is very less yearly. Equation of the fit for stationary process: \[\hat{y}_{t} = x_{t}+(3246.6875)-(1.6399)t\]

From the above graph we can say that there is no change in detrended plot and the original data acf plot, it typically means that the data is stationary. But when the first order difference is applied the high correlation is removed but there is no seasonal correlation.

As depicted in the above figure, the series is now stationary and ready for future study.